For a f-orbital, the values of m are

Options

A. `-1, 0, +1`
B. `0, +1 +2, +3`
C. `-2, -1, 0, +1, +2`
D. `-3, -2, -1, 0, +1, +2, +3`

Answer

To determine the values of the magnetic quantum number (m) for an f-orbital, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Azimuthal Quantum Number (L)**:
- For f-orbitals, the azimuthal quantum number (L) is equal to 3. This is based on the quantum number designations where:
- s = 0
- p = 1
- d = 2
- f = 3

2. **Determine the Range of Magnetic Quantum Number (m)**:
- The magnetic quantum number (m) can take on values from -L to +L, including zero. Therefore, the formula for m is:
\[ m = -L, -L + 1, ..., 0, ..., L - 1, L \]

3. **Substituting the Value of L**:
- Since L = 3 for f-orbitals, we can substitute this value into the range:
\[ m = -3, -2, -1, 0, 1, 2, 3 \]

4. **List the Values**:
- The possible values of m for the f-orbital are:
- -3
- -2
- -1
- 0
- 1
- 2
- 3

5. **Count the Total Values**:
- There are a total of 7 possible values for m.

### Final Answer:
The values of m for an f-orbital are: **-3, -2, -1, 0, 1, 2, 3**.

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